Shadowless render pass
Blender Internal:
You can exclude a pass from the Combined pass by toggling the camera icon next to the appropriate pass in Render Layers &gt; Passes:

Cycles:
The trick with cycles is that there is direct lighting and indirect lighting.
If you only want to filter out shadows, then it's as simple as dividing render by the Shadow pass with a Mix node. However, indirect lighting gets in the way of this. If you combine the Indirect pass with the Shadow pass, then use that to divide, you will remove all the indirect lighting and shadows. (you end up with a Color pass that has no shading at all).
here are some workarounds:
Renderlayers:
There might be a better way to do this, but you can use two renderlayers:
Layer 1 contains the cube object.
Layer 2 has the lights, floor and background.
Settings for Renderlayer1:
For this render layer all scene layers are enabled to render the object and background.
 
Settings for Renderlayer2:
For the no shadows layer, the scene layer with the cube is excluded and masked to remove shadows cast by the cube and to create a mask to combine with the other layer later.
 
Composite nodes:
All that remains to be done is combining the cube into the no shadows layer.
If you have Render settings &gt; Film &gt; Transparent enabled you could use an Alpha over node, or you could use a Mix node with the Alpha of the no shadows layer as a mix factor:

Material nodes:
You can filter out shadows per material with material nodes, e.g. for a shadowless and bounceless diffuse shader:

This will let light through the object when it's bounced indirectly of a diffuse object and when sent directly from a light source:

The obvious downside to this is you have to use two scenes and recreate your materials to use this for compositing.
Object shadow property:
You can also remove shadows per object by unchecking the Shadow box in the Properties Editor &gt; Object &gt; Ray Visibility:

To do this for all objects for use in compositing, you could

Create a new scene from your current scene.

A&gt; select all

After disabling the Shadow box in Object &gt; Ray Visibility, right click it and select Copy to selected to set this for all selected objects.


This will prevent all objects from casting shadows.
You can now use this scene in the compositor as a renderlayer.